McCarron finished 18-of-32 for 187 passing yards but was picked off twice for the Crimson Tide (10-0, 7-0 SEC), who used a tough defense to overcome four total turnovers.
T.J. Yeldon racked up 160 rushing yards on 24 carries.
Alabama next hosts Chattanooga before facing No. 9 Auburn in the annual Iron Bowl game.
Mississippi State (4-6, 1-5) was paced by Tyler Russell, who was 15-of-24 for 144 passing yards.